Axicon is a versatile optical element for forming a zero-order Bessel beam, including high-power laser radiation schemes. Nevertheless, it has drawbacks such as the produced beam’s parameters being dependent on a particular element, the output beam’s intensity distribution being dependent on the quality of element manufacturing, and uneven axial intensity distribution. To address these issues, extensive research has been undertaken to develop nondiffracting beams using a variety of advanced techniques. We looked at four different and special approaches for creating nondiffracting beams in this article. Diffractive axicons, meta-axicons-flat optics, spatial light modulators, and photonic integrated circuit-based axicons are among these approaches. Lately, there has been noteworthy curiosity in reducing the thickness and weight of axicons by exploiting diffraction. Meta-axicons, which are ultrathin flat optical elements made up of metasurfaces built up of arrays of subwavelength optical antennas, are one way to address such needs. In addition, when compared to their traditional refractive and diffractive equivalents, meta-axicons have a number of distinguishing advantages, including aberration correction, active tunability, and semi-transparency. This paper is not intended to be a critique of any method. We have outlined the most recent advancements in this field and let readers determine which approach best meets their needs based on the ease of fabrication and utilization. Moreover, one section is devoted to applications of axicons utilized as sensors of optical properties of devices and elements as well as singular beams states and wavefront features.

Modern Types of Axicons: New Functions and Applications.

Axicon is an interesting optical element for its optical properties. This paper presents an approach to dynamically generated tunable axicons with a spatial light modulator (SLM). 256-level phase computer-generated holograms (CGHs) were loaded into the SLM to simulate the positive and negative axicons. The intensity distributions of beams passing through these axicons were analyzed with the principle of blazed grating and Fresnel diffraction; and the diffraction patterns were obtained theoretically in terms of zero-order Bessel beams and annular hollow beams, corresponding to the positive and negative axicons, respectively. Experimental results verified that the diffraction patterns have the same distribution as the real axicon. The types of the axicon and the axicon’s parameters can be easily altered through changing the CGHs.

Tunable Axicons Generated by Spatial Light Modulator with High-Level Phase Computer-Generated Holograms

A phase differential heterodyne interferometer for simultaneous measurement of straightness error and displacement

Generation of Mathieu beams based on the detour phase encoding method

In the context of this article we demonstrate a novel Fizeau interferometric system that copes with the presence of
vibrations. Besides the conventional high spatial, but low temporal resolution detector system (the CCD camera) used in
phase shifting interferometry, an additional high temporal, but low spatial resolution detector system was integrated, in
order to measure the random phase shifts that are induced under the influence of the vibrations. The additional sensor
consists of three photodiodes. The acquired analog signals enable the measurement of the occurring phase shifts at three
non-collinear locations on the test surface. Under the assumption of the rigid body shifts and tilts of the test object, the
resulting phase shifts at the three individual locations enable the determination of the random phase shifts over the entire
image aperture. While the random oscillations of the test object are continuously measured, the CCD camera acquires
several interferograms. In consequence, a phase shifting algorithm for random phase shifts was applied. In order to prove
the validity of the new interferometer, a test surface of known topography was measured. The results of the
measurements in presence of vibrations show very good concordance with the surface data given by the supplier. The
analysis of the root mean square (RMS) over ten different measurements shows a measurement repeatability of about
0.004 waves (approximately 2.5 nm for 632.8 nm laser wavelength).

Random-phase-shift Fizeau interferometer

Measurement of four-degree-of-freedom error motions based on non-diffracting beam

Single wavelength microscopic interferometry, driven by the Piezoelectric Transducer (PZT), is a common surface topography measurement method. Its measurement accuracy is directly determined by the original phase acquisition precision of every pixels in area array CCD. Traditional phase identification methods adopt 3 points or 4 points algorithm to obtain the phase. However, they require the displacement step, actuated by the PZT, to strictly keep the same to satisfy the 90° phase condition. Therefore, these methods are only suitable for the strict anti-vibration experimental environment or conditions with high precise closed-loop PZT actuator and strict calibration of interferometric wavelength. An auto-acquisition driving step method for the single wavelength microscopic interferometry is presented in this paper. Firstly, interference sequence diagrams, containing the surface topography information, are gathered by the CCD under open-loop PZT actuating. Next, two pixels whose phase difference is approximate 90° are selected as the calculating center to obtain smoothed gray values with regional gray average algorithm, which can reduce the influence of random noise. Finally, an optimal fitting algorithm for the ellipse, formed by the average gray values, is proposed to obtain the amplitudes and offsets of the two gray values array. According these fitting parameters and gray values, the drive step can be calculated by elliptic equations. Experiments have shown that this method can reduce the requirement conditions of measurement conditions and improve the measurement accuracy.

Xuanze Wang

Papers

Measurement of four-degree-of-freedom error motions based on non-diffracting beam

Tunable Axicons Generated by Spatial Light Modulator with High-Level Phase Computer-Generated Holograms

A driving step auto-access method for single-wavelength microscopic interference

The Least-squares Algorithm for Interferograms with Random Phase Shifts